Rectangles for proof of Difference of Squares Formula 

						var board = JXG.JSXGraph.initBoard('box1', {
boundingbox: [-10, 10, 10, -10],showNavigation:false, showcopyright: false, axis: false,
});

var p1 = board.create('point', [-8, -4],{face:'',label:{offset:[-50,0]}});
var p2 = board.create('point', [2, -4],{face:'',name:'',label:{offset:[10,0]}});
var pol1 = board.create('regularpolygon', [p1, p2, 4],{fillcolor:"red",vertices:{face:'',name:''}});

var l1 = board.create('segment', [p1,p2]);
var g1 = board.create('glider', [-4, 1.5, l1],{name:''});
var l2 = board.create('segment', [p1,g1],{withLabel:true,name:"b",label:{offset:[0,-15]}});
var pol2 = board.create('regularpolygon', [p1, g1, 4],{vertices:{face:'',name:''}});

var p3 = board.create('point', [function(){return pol1.vertices[2].X()+l2.L();}, function(){return pol1.vertices[2].Y();}],{face:'',name:''});

var p4 = board.create('point', [function(){return p3.X();},function(){return pol2.vertices[2].Y();}],{face:'',name:''});

var l3 = board.create('segment', [pol1.vertices[1],pol1.vertices[2]]);

 var pp1 = board.create('perpendicularpoint', [p4, l3],{face:'',name:''});
 var pol3 = board.create('polygon', [pp1, pol1.vertices[2], p3, p4],{fillcolor:"#00FF00",});

var pol4 = board.create('polygon', [g1,p2, pp1, pol2.vertices[2]],{fillcolor:"#EEE"});

var l4 = board.create('segment', [pol1.vertices[3],pol1.vertices[2]],{withLabel:true,name:"a"});
var l5 = board.create('segment', [pol1.vertices[3],pol1.vertices[4]],{withLabel:true,name:"a",label:{offset:[-20,0]}});
var l6 = board.create('segment', [pol1.vertices[2],p3],{withLabel:true,name:"b",label:{offset:[0,10]}});
var l7 = board.create('segment', [p3,p4],{withLabel:true,name:"a-b",label:{offset:[10,0]}});

//alert(l2.L()+"\n"+l6.L())
var l8 = board.create('segment', [pp1,pol2.vertices[2]],{withLabel:true,name:"a-b",label:{offset:[-10,10]}});

The image appears in the following posts

  1. The difference of squares is one of standard algebraic identities, which is used to factorize the terms like

    a^2-b^2
    (1)

    That is, the difference of two squared terms is equal to the product of the sum of the two terms and the difference of the two terms. The difference of squares is commonly given as,

    a^2-b^2=(a+b)(a-b)
    (2)

    The formula can be used for factoring polynomials with the square of one term minus the square of another. Before diving in the complex examples, let's find out different ways to prove the formula of the difference of squares, which can be done algebraically and geometrically.

Triangle posted 1 year ago

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